Anticommutator for a Nonlinear Field Theory

Abstract

The anticommutator for the Thirring model is computed by ordering the operator $\psi \mathrm{}\left(x\right)\mathrm{}{\psi }^{*}\left(x^{\prime }\right)$ and evaluating its renormalized vacuum expectation value. The infrared divergence is defined by introducing an ad hoc cutoff. The final expression does not agree with the approximations obtained by using perturbation theory or by using expansion over intermediate states (with the same cutoff). It is also found that Heisenberg's procedures cannot be applied to this two-dimensional problem.